Magnetic Raman Scattering of Insulating Cuprates

We study the $B_{1g}$ and $A_{1g}$ Raman profiles of M$_{2}$Cu$O_{4}$ (with M= La, Pr, Nd, Sm, Gd), Bi$_{2}$Sr$_{2}$Ca$_{0.5}$Y$_{0.5}$Cu$_{2}$O$_{8+y}$%, YBa$_{2}$Cu$_{3}$O$_{6.2}$ and PrBa$_{2}$Cu$_{2.7}$Al$_{0.3}$O$_{7}$ insulating cuprates within the Loudon-Fleury theory, in the framework of an extended Hubbard model for moderate on-site Coulomb interaction $U$. We calculate the non-resonant contribution to these Raman profiles by using exact diagonalization techniques and analyze two types of contributing mechanisms to the line shapes: 4-spin cyclic exchange and spin-phonon interactions. Although these interactions contribute to different parts of the spectra, together, they account for the enhanced linewidth and asymmetry of the $B_{1g}$ mode, as well as the non-negligible intensity of the $A_{1g}$ Raman line observed in these materials.